On the physical Hilbert space of QCD$_2$ in the decoupled formulation

TL;DR

This paper investigates the structure of the physical Hilbert space in two-dimensional quantum chromodynamics (QCD$_2$) using a decoupled formulation, identifying the necessary conditions for physical states.

Contribution

It systematically determines which nilpotent Noether charges must vanish on physical states in the decoupled QCD$_2$ formulation, clarifying the Hilbert space structure.

Findings

Identifies the subset of Noether charges that must vanish on physical states.

Analyzes the implications for the Hilbert space structure in QCD$_2$.

Provides a systematic approach to understanding physical state conditions.

Abstract

We consider the QCD$_2$ partition function in the non-local, decoupled formulation and systematically establish which subset of the nilpotent Noether charges is required to vanish on the physical states. The implications for the Hilbert space structure are also examined.